When temperature (T) is lower than the T_c, the energy of spin parallel
orientation is higher
than spin antiparallel orientation. From the well-known expressions of entropy
of mixing, the entropy
for spin-parallel orientation is lower than that of spin antiparallel
orientation. One expects a static structure of spin
antiparallel orientation when T becomes lower than T_c. However, the
observed ferromagnetism is just the
opposite phenomena. Clearly there is a big flaw in statistical physics, which is
the Gibbs paradox
statement (Entropy of mixing to form solid assemblages, liquid and gas mixtures
or any other
analogous assemblages such as mixed quantum states, decreases with the increase
in the property
similarity of the subsystems). A new entropy theory says that the entropy of
mixing increases
continuously with the increase in similarity [1,2]. Indistinguishability and
maximum symmetry
corresponds to the maximal entropy of mixing. The logarithmic relations of
entropy and symmetry
were established [1]. Indistinguishability and symmetry is an ubiquitous driving
force for all
spontaneous physical and chemical processes. This new theory conforms very well
with and explains
perfectly all the symmetry breaking phenomena. [1] S. -K. Lin, J. Chem. Inf.
Comp. Sci. 36 (1996)
367-376. [2] S. -K. Lin, J. Theor. Chem., 1 (1996) 135-150; S. -K. Lin,
Molecules, 1 (1996) 57-67.
(Downloadable from
www.mdpi.org/lin.htm).